> Okay, so again, what do we do? Punishment is out. How do we get people to simply desire to do better?
Provide a bloody baseline. Every child deserves an environment they are given everything that a child needs to succeed, regardless of how fucked their home life is. The state can only control what happens outside of school so much, but it can control what happens in school.
It means transportation to and from school, or walkable access to them. It means school lunches. It means a space to work and study. It means a space that is safe and free from antisocial disruption. It means dealing with the antisocial disruption, through the counseling and support services children need.
You can't fix every broken human being, but you can not just abandon them after putting in minimal effort.
> Education is free and lower income areas generally have more school funding.
That delta is nowhere near enough, because the job of educating a child with an absolutely fucked home life is monumentally harder than one who doesn't have one. But it's necessary to do it, to work on the problem long-term.
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> How do we get people to value themselves and their families, much less something abstract like our republic?
Teach them to be a part of their community. Put them to meaningful work that improves it. This is huge for social cohesion, and every high-cohesion society or high-cohesion subculture in a low-cohesion society does it.
For a trivial example, Japanese students don't clean their classrooms because their schools are too cheap to hire janitors. There's no shortage of that kind of work that children can meaningfully do that improves them, their environment, and their town, and gives them a reason to give a shit about it.
Clubs are another. The level of support and funding for them dramatically falls short of where they should be. They should not be an optional activity largely available and patronized by the college-application-padding upper-middle-class. They are necessary for proper development.
You can also attack the problem from the other direction - doing less to actively create broken families and households. There's an incredible perception of unfairness in society, and reasonable people will treat it the same way that they feel it treats them.